Question

The chief of security for Mall of the Dakotas was directed to study the problem of missing goods. He selected a sample of 120 boxes that had been tampered with and ascertained that, for 60 of the boxes, the missing pants, shoes, and so on were attributed to shoplifting. For 35 other boxes, employees had stolen the goods, and for the remaining 25 boxes he blamed poor inventory control. In his report to the mall management, can he say that shoplifting is twice as likely to be the cause of the loss as compared with either employee theft or poor inventory control and that employee theft and poor inventory control are equally likely? Use the 0.01 significance level.

H₀: The proportions are as stated.      H₁: The proportions are not as stated.

State the decision rule using 0.01 significance level. (Round your answer to 3 decimal places.)

Compute the value of chi-square. (Round your answer to 3 decimal places.)

What is your decision regarding H₀?

Answer 1

1)

Decision rule: reject Ho if value of test statistic X2>9.210

2)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
shoplifting	0.500	60.000	60.000	0.00	0.000
stolen	0.250	35.000	30.000	0.91	0.833
poor inventory control	0.250	25.000	30.000	-0.91	0.833
total	1.000	120	120		1.6667
test statistic X2 =		1.667

fail to reject null hypothesis